It looks like this is not going to be possible. On the plus side, the order of the fonts that *are* displayed in the typography short-code drop-down can be fixed with a single line of code in dialog-js-.php
What I would suggest trying, is inserting the short-code for any other random font, then manually changing the font name in the short-code to your desired Google font. I have not tried that yet, but if the short-code is working properly, it should load up the font into tha page at run-time and work. You can get the full font names from the settings page of this plugin.
Edit: yes it does work. I inserted this into a page:
[typography font="Cantarell" size="24" size_format="px"]Test typography[/typography]
then changed it to this:
[typography font="Herr Von Muellerhoff" size="24" size_format="px"]Test typography[/typography]
and got the desired cursive font.
So in conclusion: you can use any Google Webfont for any text in any page or post. You cannot select from all available fonts in the Woothemes short-code generator, at least not without some changes to the core Woo Framework, which is out of my hands.